The role of leader of Europe’s awkward squad, played with aplomb by the UK for the past 45 years, will be handed to Poland and Hungary at the weekend when European Union leaders meet in Rome to celebrate 60 years of the EU’s existence and map out a new future after Brexit.

With Theresa May absent, leaders from Warsaw and Budapest will puncture any mood of self-congratulation. They are also expected to bridle at any plans to empower groups of member states to choose to integrate more deeply, in effect creating a two-speed Europe.

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But Poland’s assertiveness, says Gavin Rae, an associate professor at the Kozminski University in Warsaw, “reflects a fear about a wider potential change in the balance of power in the wake of the Brexit referendum” as it loses one of its closest allies and “finds itself more isolated than ever”.

It fears a two-speed Europe might institutionalise this process of marginalisation. “We cannot accept any announcements of a two-speed Europe,” said Jarosław Kaczyński, the chair of the ruling Law and Justice (PiS) party, who met May this week. “This would mean either pushing us out of the European Union or downgrading us to an inferior category of members.”

Viktor Orbán, the Hungarian prime minister, has dismissed a two-speed Europe as an affront to eastern Europe. Poland, the Czech Republic, Slovakia and Hungary – the Visegrád Four – joined the EU to be at the core of Europe, not its periphery.

Hungary’s prime minister Viktor Orbán has dismissed the idea of a two-speed Europe as an affront to eastern Europe. Photograph: Thierry Charlier/AFP/Getty Images

The Polish prime minister, Beata Szydło, on Thursday threatened not to sign the Rome declaration if it did not include issues that were priorities for Poland, including EU unity, the priority of Nato, strengthening national parliaments and a unified single market. A form of words may be found to paper over the cracks, but according to Piotr Buras, the director of the European Council on Foreign Relations in Warsaw, the trajectory is one of divergence.

Poland and Hungary regard their role as telling home truths to the old European elite in the interests of the EU’s own survival. From the perspective of Szydło and Orbán, it is they who been proved right about what the Hungarian prime minister called the “terrorist Trojan horse of mass migration”, the impracticality of compulsory migrant quotas and the necessity of asylum camps, hard borders and national self-determination.

Far from being isolated nationalist mavericks, they believe themselves to have been leading a necessary counter-revolution. In a recent interview in the Hungarian weekly Heti Válasz, Kaczyński said that cooperation among the countries of central and eastern Europe could serve as a counterweight to the current leadership in Brussels.

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Yet at first glance, the revived idea of a flexible or multi-speed Europe, promoted by France and Germany, with “different circles for cooperation” might be an idea Poland could welcome. No country is being ordered to cooperate. Countries might choose to pool greater sovereignty on issues such as defence, Euro governance or migration.

This live and let live approach appears to have been rejected by Poland and Hungary. Buras describes the Polish position as “completely inconsistent”. They favour flexibility in theory, but fear that if the core group cooperates more, they will lose out.

The Polish foreign minister, Witold Waszczykowski, said this week: “The risk is that the eurozone will create its own structures, its own budget and will dominate over the rest of Europe.”

Desperate for the EU to be seen to deliver, Germany and France want to remove roadblocks to effectiveness, and are losing patience with the east. The French president, François Hollande, warned the Poles at the last EU summit: “You may have your principles, but we have the structural funds.” The fact that Angela Merkel is willing to countenance a two-speed Europe, something she seemed reluctant to back previously, is an indication of her frustration with Poland.

Some commissioners are calling for the EU to withdraw Poland’s EU funding unless it drops judicial reforms seen as flouting democratic norms and, for good measure, accepts the 6,200 migrants it was allocated by Brussels. Such threats are not trivial. Poland is by far the EU’s largest net recipient of funds. It receives almost a quarter of all EU funding, accounting for 2.3% of its gross domestic product.

The leading liberal MEP Guy Verhofstadt said this week: “The EU is a community of the rule of law. We must not stand aside and watch this any longer.”

But Poland so far does not look like a country preparing to back down in the face of what it regards as blackmail. Its attempt to block the reappointment of fellow Pole Donald Tusk as EU council president bordered on fiasco, with no country, not even the Visegrád Group coming to its support.

The Poles responded to the rebuff by refusing to sign the summit conclusions, an unprecedented step. It promised in future to “bare its sharp teeth” while the nationalist paper Gazeta Polska ran a cover story with Tusk wearing the uniform of the Wehrmarcht.

The best hope for Brussels may be that there is an internal political reaction after years in which both governments have consolidated power around growing economies, conservative social reform and nationalism.

Faint stirrings of internal dissent are visible in both countries. In Poland, one poll published on Monday showed support for PiS had fallen five points to 29%, while Tusk’s Civic Platform was up 10 points to 27%. The possibility of Tusk returning to contest the presidency in 2020 is not far-fetched.

In Hungary, due to go to the polls next year, a new party vowing to be neither right nor left has been formed called the Momentum Movement, led by 28-year-old András Fekete-Győr. Momentum stopped Budapest’s bid for the Olympic Games in 2024, attracting 260,000 signatures, and already has the whiff of a party capable of usurping a tired political establishment.

But Rae argues that for the conservative forces to lose popularity requires the EU to adopt an economic strategy to help those in Poland and Hungary that want to cooperate with it.

A crude version of a two-speed Europe, in which only the euro countries prosper, might just encourage the sense of grievance on which populism thrives.